Roth vs. Traditional IRAs: The Tax Trade-Off Isn't Always What You Think

"That is, the account type can be chosen to obtain a higher expected ATA but not lower ATA uncertainty," Hulse says. "It can instead be chosen to obtain lower ATA uncertainty but not higher expected ATA."

According to Hulse, in some situations, there is a clear trade-off that must be made. One can pursue a higher expected ATA but more ATA uncertainty for a traditional account, or they can seek to capture a lower expected ATA but lower ATA uncertainty for a Roth account.

In other situations, the variance of the ATA is actually lower for a traditional account than for a Roth account. This happens when the tax rate is expected to increase by more than a small amount. However, a Roth account has a higher mean ATA than a traditional account in the same situation, Hulse finds, which means there is another trade-off: a higher expected ATA but more ATA uncertainty for a Roth account versus a lower expected ATA but lower ATA uncertainty for a traditional account.

Ultimately, the trade-off between the expected ATA and its uncertainty relates to the fact that the ATA's variance can be lower for a traditional account contribution than for a Roth account contribution.

A Case Study

Hulse steps through several theoretical case studies to show how these dynamics work in practice. In one case, a theoretical retirement saver has $10,000 of before-tax income to contribute, and her current tax rate is 24%. This person, thus, can contribute either $7,600 to a Roth account or $10,000 to a traditional account.

Because of the government's budget deficits, the individual and her advisor believe that tax rates are likely to increase in the future, but they are unsure about the extent of the increase. She believes her future tax rate has a 20% chance of being 24% (no increase), a 40% chance of being 28% and a 40% chance of being 32%.

Hulse computes that this individual's uncertain future tax rate thus has a mean of 28.8% and a variance of approximately 0.09%, with a 2.99% standard deviation.

For the investments in her Roth or traditional account, the investor believes there is a 26% chance that each dollar contributed grows to $1.50, a 48% chance it grows to $2.65 and a 26% chance it grows to $4.66. As Hulse explains, this person thus has nine possible combinations of future tax rates and growth figures.

The analysis shows the ATA's mean for these outcomes is $21,839 for a Roth account and $20,460 for a traditional account. The mean is higher for a Roth account, consistent with the expected tax rate increase from 24% to 28.8%. Notably, the ATA's variance for a Roth account is meaningfully higher than the variance for the traditional account, with the standard deviations being $8,812 and $8,307, respectively.

Thus, this person faces a trade-off between a Roth account's higher expected ATA and a traditional account's lower ATA uncertainty. In another example covered in the paper, the opposite turns out to be true, which Hulse says shows the importance of more nuanced and individualized retirement planning.

Drawing Conclusions

In conclusion, Hulse says, the new analysis shows that the type of account with the higher expected after-tax accumulation generally also has higher uncertainty for it. This means there generally is a trade-off that clients will have to make between these two considerations.

If an individual chooses the account type with the higher expected accumulation, they generally must accept higher uncertainty, Hulse says. If an individual chooses the account type with lower uncertainty, they generally must accept a lower expected accumulation.

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